Question 1

Mike was granted stock options on 1,000 shares of his employer's stock. The stock is currently selling for $27.70 a share and has a standard deviation of 36 percent. The option's strike price is $27.50 and the time to maturity is 10 years. What is the value of each option given a risk-free rate of 3 percent? Assume that no dividends are paid.

Accepted Answer

11ea6d0e_c3d5_7f38_b3c7_b7f401715c93_TB1223_00

Question 2

You own 4,800 shares of a stock that is currently priced at $34 a share. Given this price, the option delta for a $30 call option on this stock is .955. How many $30 call option contracts do you need to hedge against a -$1 change in the price of the stock?

Accepted Answer

The answer of You own 4,800 shares of a stock...

Question 3

Draw a graph with the option price on the vertical axis and the time to expiration on the horizontal axis. Illustrate how put and call option prices vary as the time to expiration increases.

Accepted Answer

The answer of Draw a graph with the option price...

Question 4

You have been granted stock options on 200 shares of your employer's stock. The stock is currently selling for $36.15 and has a standard deviation of 28 percent. The option's strike price is $35 and the time to maturity is 10 years. What is the value of each option given a risk-free rate of 4.5 percent? Assume that no dividends are paid.

Accepted Answer

The answer of You have been granted stock options on...

Question 5

You own 2,000 shares of ABC stock that is currently priced at $27 a share. Given this price, the option delta for a $25 call option on this stock is .718. How many $25 call options do you need to hedge against a -$1 change in the price of the stock?

Accepted Answer

To hedge against a -$1 change in the price of the stock, we need to calculate the total delta we have to hedge, which is:
Total delta = number of shares x delta per share
Total delta = 2,000 x 0.718
Total delta = 1,436
Since the delta of a call option is positive, we need to buy put options to hedge against a price drop. To calculate the number of put options we need, we divide the total delta we need to hedge by the delta per option, which is:
Number of put options = total delta / delta per option
Number of put options = 1,436 / 0.517
Number of put options = 2,786
Therefore, we need to write 2,786 $25 put options to hedge against a -$1 change in the price of the stock. The closest answer choice is D.

Question 6

You own 9,500 shares of GO stock which is currently valued at $48 a share. The $50 put has a premium of $2.50 and a put delta of -.58. What position should you take in $50 put contracts to hedge your stock against a $1 decrease in price?

Accepted Answer

To hedge against a $1 decrease in stock price, you need to offset the loss in stock value with gains from the put options. The delta of the put is -0.58, meaning each put option will gain $0.58 for every $1 decrease in stock price. You own 9,500 shares, so a $1 decrease results in a $9,500 loss. To offset this, you need 9,500 / 58 = 163.79, rounded to 163 contracts (since each contract covers 100 shares).

Question 7

You have an equity portfolio valued at $1.78 million that has a beta of 1.28. You have decided to hedge this portfolio using SPX call option contracts. The S&P 500 index is currently 1390. The option delta is .6435. How many option contracts must you write to effectively hedge your portfolio?

Accepted Answer

The answer of You have an equity portfolio valued at...

Question 8

You own 1,200 shares of Banner Co. stock that is currently priced at $42 a share. Given this price, the option delta for a $40 call option on this stock is .664. How many $40 call options do you need to hedge against a -$1 change in the price of the stock?

Accepted Answer

The answer of You own 1,200 shares of Banner Co....

Question 9

Identify the five factors of the Black-Scholes option pricing model and identify whether each factor must increase or decrease to cause the price of a put option to increase.

Accepted Answer

The answer of Identify the five factors of the Black-Scholes...

Question 10

Laura has an equity portfolio valued at $11.2 million that has a beta of 1.32. She has decided to hedge this portfolio using SPX call option contracts. The S&P 500 index is currently 1402. The option delta is .582. How many option contracts must Laura write to effectively hedge her portfolio?

Accepted Answer

To hedge the portfolio, Laura needs to sell call options on the S&P 500 index. The number of contracts she needs to sell can be calculated as follows:

Total value of portfolio / (index level x option delta x multiplier)

Given: 
Total value of portfolio = $11.2 million 
Index level = 1402 
Option delta = 0.582 
Multiplier = 100 (each SPX option contract covers 100 shares of the index)

Therefore:

Number of contracts = $11.2 million / (1402 x 0.582 x 100) 
= 181.07

Since Laura cannot sell a fraction of a contract, she would need to sell 181 SPX call option contracts to effectively hedge her portfolio. Therefore, the answer is D, 181 contracts.

Question 11

You own 1,800 shares of Textile stock which is currently valued at $62 a share. The $65 put has a premium of $4.26 and a put delta of -.60. What position should you take in $65 put contracts to hedge your stock against a $1 decrease in price?

Accepted Answer

To hedge against a $1 decrease in price, we need to protect 1,800 shares multiplied by $1, which gives us a total of $1,800. 
The put delta is -.60, which means that for every $1 decrease in stock price, the put option will increase in value by $0.60. Therefore, to cover the required $1,800, we need:

$1,800 / ($0.60 premium per $1 decrease) = 3,000 total options 
3,000 / 100 (number of options each contract has) = 30 contracts

Thus, the best choice is to buy 30 contracts.

Question 12

Create a stock price tree for three periods for a stock that is currently valued at $10 a share. The up amount per period is 1.15 and the down amount per period is .90. Show all dollar amounts to 3 decimal places.

Accepted Answer

The answer of Create a stock price tree for three...

Quiz 16: Option Valuation